Killing Spinor Equations from Nonlinear Realisations

Starting from a nonlinear realisation of eleven dimensional supergravity based on the group G11, whose generators appear as low level generators of E11, we present a super extended algebra, which leads to a covariant derivative of spinors identical to the Killing spinor equation of this theory. A similar construction leads to the Killing spinor equation of N=1 pure supergravity in ten dimensions.